[R] Ellipse that Contains 95% of the Observed Data

[Bert Gunter]

Tom:

You asked whether two groups have the same underlying population 1st and 2nd
moments. The answer is: no they don't. Nothing is ever exactly the same as
anything else (indeed, I think this is the Paul Exclusion Principle ;-)  ). 

So quoting Jim Holtman: "What is the question?" That certainly requires
someone who knows something about the scientific issues (not me!). But maybe
it's something like: "Well, if these two **populations** are more different
than a, b, c, ... in population characteristics A, B, and C,...  then that
is scientifically meaningful."  So then you can ask: "Well how can I
measure/statistically characterize  A,B, and C,...? -- How much uncertainty
will there be in this characterization (depends on study design and how one
characterizes "uncertainty" ) and how much can I tolerate and still reach
scientifically useful conclusions."  

And so forth... all of which might be squeezed into Bayesian, or classical,
parametric, nonparametric, or whatever holes happen to satisfy your
particular "religious" convictions. Or, perhaps even better, be informed by
some good plots (horrors -- no P-Values! ...  but those are **my** religious
convictions). But those are mere statistical details, about which all I can
safely say is: The question is not "Are they the same?"

Cheers,

Bert Gunter
Genentech Nonclinical Biostatistics

P.S. Technical comment (because, alas, I **are** a statistician): You
probably want the ellipsoids you speak of to cover subsets of the
**populations** with some degree of certainty, not of the **data.**
  
Disclaimer: Bert Gunter's opinions only. Associate neither my company nor my
colleagues with my obstreperousness.



-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On
Behalf Of Tom La Bone
Sent: Monday, March 29, 2010 9:56 AM
To: r-help at r-project.org
Subject: Re: [R] Ellipse that Contains 95% of the Observed Data


I know what "get a bigger sample means". I have no clue what "ask a more
statistically meaningful question" means. Can you elaborate a bit?

Tom
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